Two-point AG codes from one of the Skabelund maximal curves

In this paper, we investigate two-point Algebraic Geometry codes associated to the Skabelund maximal curve constructed as a cyclic cover of the Suzuki curve. In order to estimate the minimum distance of such codes, we make use of the generalized order bound introduced by P. Beelen and determine certain two-point Weierstrass semigroups of the curve.Comment: 15 page

AG codes and AG quantum codes from the GGS curve

In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all $\mathbb F_{q^2}$-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes

Locally recoverable codes from automorphism groups of function fields of genus g≥1g \geq 1

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have $\delta$ non overlapping subsets of cardinality $r_i$ that can be used to recover the missing coordinate we say that a linear code $\mathcal{C}$ with length $n$, dimension $k$, minimum distance $d$ has $(r_1,\ldots, r_\delta)$-locality and denote it by $[n, k, d; r_1, r_2,\dots, r_\delta].$ In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality $r_i+1$ of the automorphism group of a function field $\mathcal{F}| \mathbb{F}_q$ of genus $g \geq 1$, we propose a construction of $[n, k, d; r_1, r_2,\dots, r_\delta]$-codes and apply the results to some well known families of function fields

New examples of maximal curves with low genus

We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$, $5$ and $10$. As a corollary, explicit equations for curves that are either maximal or minimal over the finite field with $p^2$ elements are obtained for infinitely many $p$'s. Lists of small $p$'s for which maximality holds are provided. In some cases we describe the automorphism group of the curve

Multi point AG codes on the GK maximal curve

In this paper we investigate multi-point Algebraic\u2013Geometric codes associated to the GK maximal curve, starting from a divisor which is invariant under a large automorphism group of the curve. We construct families of codes with large automorphism groups